Where is the hinge point? & what is the moment of inertia of a square?

In summary: Good luck!In summary, a uniform wire of length 2a with a linear mass density λ is placed on a smooth horizontal surface. An impulse J is applied at one end, causing the system to rotate about the midpoint P of the wire. The point of application of the impulse is considered the hinge point, and the center of mass of the wire will undergo both translational and rotational motion after the impulse is delivered. The angular velocity of the system just after the impulse can be found using the conservation of angular momentum equation, Iω = Jr, where R is the perpendicular distance from the hinge point to the point of application of the impulse.
  • #1
randomgamernerd
139
4

Homework Statement

:[/B] A uniform wire of linear mass density λ having three sides each of length 2a is kept on a smooth horizontal surface. An impulse J is applied at one end as shown in the figure. P is the midpoint of AB. Now answer the following questions.
1) The angular velocity of system just after the impulse?

Sorry the image is poorly lit.

Homework Equations

: [/B]Conservation of angular momentum, Iω = Jr
Where R is perpendicular distance of Point of application of J from hinge point.

The Attempt at a Solution

:[/B]
I want to know which point should i consider hinge point. Is it the other end of the rod commected to B and⊥ AB?
 

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  • #2
randomgamernerd said:
I want to know which point should i consider hinge point. Is it the other end of the rod commected to B and⊥ AB?
If you have watched a juggler juggling bowling pins, lit torches or chain saws, about what point would you see these items rotate? Note that the impulse is given very near one end. More specifically, what point (if any) would undergo projectile motion?
 
  • #3
kuruman said:
If you have watched a juggler juggling bowling pins, lit torches or chain saws, about what point would you see these items rotate? Note that the impulse is given very near one end. More specifically, what point (if any) would undergo projectile motion?

Centre of mass? So i consider the COM as the hinge point?
 
  • #4
Yes. After the impulse is delivered, the COM will execute translational motion while simultaneously there will be rotational motion about the COM.
 
  • #5
kuruman said:
Yes. After the impulse is delivered, the COM will execute translational motion while simultaneously there will be rotational motion about the COM.

O ho, thanks, i will try solving the sum now, and if the answer I get does not match, then I will post my work here again [emoji28]
 
  • #6
randomgamernerd said:
O ho, thanks, i will try solving the sum now, and if the answer I get does not match, then I will post my work here again [emoji28]
Sounds like a plan.
 

1. Where is the hinge point located on a square?

The hinge point on a square is located at the intersection of two sides, also known as the vertex. This is the point where the square can rotate freely around.

2. How is the hinge point determined on irregularly shaped objects?

The hinge point on irregularly shaped objects can be determined by finding the centroid of the object. The centroid is the point that divides the object into two equal areas and is also known as the center of mass.

3. What is the moment of inertia of a square?

The moment of inertia of a square depends on the mass distribution of the object and the distance of the object from the axis of rotation. It is a measure of an object's resistance to rotational motion and is calculated by the sum of the square of the distance of each mass element from the axis of rotation.

4. How does the moment of inertia of a square affect its rotation?

The moment of inertia of a square directly affects its rotation. Objects with a higher moment of inertia require more force to rotate and have a slower rate of rotation, while objects with a lower moment of inertia require less force and have a faster rate of rotation.

5. Can the moment of inertia of a square be changed?

Yes, the moment of inertia of a square can be changed by altering the mass distribution or the axis of rotation. For example, moving the axis of rotation closer to the center of mass will decrease the moment of inertia, making the object easier to rotate.

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